Simple Harmonic Motion - rearranging equation

AI Thread Summary
The discussion focuses on rearranging the equation for frequency in simple harmonic motion, f = (1/2π)√(k/m). A participant attempts to isolate variables, specifically expressing k in terms of f and m. The conversation highlights the importance of understanding the intention behind rearranging the equation, such as achieving a linear relationship between variables. Ultimately, the participant confirms they successfully figured out how to rearrange the equation to find k. The thread emphasizes the relevance of context in mathematical manipulation.
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Homework Statement


How to rearrange following equation?

Homework Equations


f = (1/2pi) square root of (k/m)

The Attempt at a Solution


(f^2 x m)/ (1/2pi)^2

Is this how i would do it?
 
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Depends on what your intention is :smile:
Do you vary something and measure something else, and want to obtain a linear relationship ?
 
BvU said:
Depends on what your intention is :smile:
Do you vary something and measure something else, and want to obtain a linear relationship ?
Thanks, I wanted to find k but worked out how to rearrange it :)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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